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## -*- texinfo -*-
## @deftypefn  {} {} shrinkfaces (@var{p}, @var{sf})
## @deftypefnx {} {@var{nfv} =} shrinkfaces (@var{p}, @var{sf})
## @deftypefnx {} {@var{nfv} =} shrinkfaces (@var{fv}, @var{sf})
## @deftypefnx {} {@var{nfv} =} shrinkfaces (@var{f}, @var{v}, @var{sf})
## @deftypefnx {} {[@var{nf}, @var{nv}] =} shrinkfaces (@dots{})
##
## Reduce the size of faces in a patch by the shrink factor @var{sf}.
##
## The patch object can be specified by a graphics handle (@var{p}), a patch
## structure (@var{fv}) with the fields @qcode{"faces"} and @qcode{"vertices"},
## or as two separate matrices (@var{f}, @var{v}) of faces and vertices.
##
## The shrink factor @var{sf} is a positive number specifying the percentage
## of the original area the new face will occupy.  If no factor is given the
## default is 0.3 (a reduction to 30% of the original size).  A factor greater
## than 1.0 will result in the expansion of faces.
##
## Given a patch handle as the first input argument and no output parameters,
## perform the shrinking of the patch faces in place and redraw the patch.
##
## If called with one output argument, return a structure with fields
## @qcode{"faces"}, @qcode{"vertices"}, and @qcode{"facevertexcdata"}
## containing the data after shrinking.  This structure can be used directly
## as an input argument to the @code{patch} function.
##
## @strong{Caution:}: Performing the shrink operation on faces which are not
## convex can lead to undesirable results.
##
## Example: a triangulated 3/4 circle and the corresponding shrunken version.
##
## @example
## @group
## [phi r] = meshgrid (linspace (0, 1.5*pi, 16), linspace (1, 2, 4));
## tri = delaunay (phi(:), r(:));
## v = [r(:).*sin(phi(:)) r(:).*cos(phi(:))];
## clf ()
## p = patch ("Faces", tri, "Vertices", v, "FaceColor", "none");
## fv = shrinkfaces (p);
## patch (fv)
## axis equal
## grid on
## @end group
## @end example
##
## @seealso{patch}
## @end deftypefn

function [nf, nv] = shrinkfaces (varargin)

  if (nargin < 1 || nargin > 3)
    print_usage ();
  endif

  sf = 0.3;
  colors = [];
  p = varargin{1};

  if (isscalar (p) && isgraphics (p, "patch") && nargin < 3)
    faces = get (p, "Faces");
    vertices = get (p, "Vertices");
    colors = get (p, "FaceVertexCData");
    if (nargin == 2)
      sf = varargin{2};
    endif
  elseif (isstruct (p) && nargin < 3)
    faces = p.faces;
    vertices = p.vertices;
    if (isfield (p, "facevertexcdata"))
      colors = p.facevertexcdata;
    endif
    if (nargin == 2)
      sf = varargin{2};
    endif
  elseif (ismatrix (p) && nargin >= 2 && ismatrix (varargin{2}))
    faces = p;
    vertices = varargin{2};
    if (nargin == 3)
      sf = varargin{3};
    endif
  else
    print_usage ();
  endif

  if (! isscalar (sf) || sf <= 0)
    error ("shrinkfaces: scale factor must be a positive scalar");
  endif

  nc = columns (vertices);
  if (nc < 2 || nc > 3)
    error ("shrinkfaces: only 2-D and 3-D patches are supported");
  endif

  m = columns (faces);
  if (m < 3)
    error ("shrinkfaces: faces must consist of at least 3 vertices");
  endif

  v = vertices(faces'(:), :);
  if (isempty (colors) || rows (colors) == rows (faces))
    c = colors;
  elseif (rows (colors) == rows (vertices))
    c = colors(faces'(:), :);
  else
    c = [];  # Discard inconsistent color data.
  endif
  sv = rows (v);
  ## We have to deal with a possibly very large number of vertices, so use
  ## sparse as midpoint (1/m, ..., 1/m) in generalized barycentric coordinates.
  midpoints = full (kron (speye (sv / m), ones (m, m) / m) * sparse (v));
  v = sqrt (sf) * (v - midpoints) + midpoints;
  f = reshape (1:sv, m, sv / m)';

  switch (nargout)
    case 0
      if (ishghandle (p))
        ## avoid exceptions
        set (p, "FaceVertexCData", [], "CData", [],
                "Vertices", v, "Faces", f, "FaceVertexCData", c);
      else
        nf = struct ("faces", f, "vertices", v, "facevertexcdata", c);
      endif
    case 1
      nf = struct ("faces", f, "vertices", v, "facevertexcdata", c);
    case 2
      nf = f;
      nv = v;
  endswitch

endfunction


%!demo
%! clf;
%! faces = [1 2 3; 1 3 4];
%! vertices = [0 0; 1 0; 1 1; 0 1];
%! patch ("Faces", faces, "Vertices", vertices, "FaceColor", "none");
%! fv = shrinkfaces (faces, vertices, 0.25);
%! patch (fv);
%! axis auto;   # Kludge required for Octave
%! axis equal;
%! title ("shrinkfaces() on triangular shapes");

%!demo
%! clf;
%! faces = [1 2 3 4; 5 6 7 8];
%! vertices = [0 0; 1 0; 2 1; 1 1; 2 0; 3 0; 4 1; 3.5 1];
%! patch ("Faces", faces, "Vertices", vertices, "FaceColor", "none");
%! fv = shrinkfaces (faces, vertices, 0.25);
%! patch (fv);
%! axis auto;   # Kludge required for Octave
%! axis equal;
%! grid on;
%! title ("shrinkfaces() on rhomboid shapes");

%!demo
%! clf;
%! faces = [1 2 3 4];
%! vertices = [-1 2; 0 0; 1 2; 0 1];
%! patch ("Faces", faces, "Vertices", vertices, "FaceColor", "none");
%! fv = shrinkfaces (faces, vertices, 0.25);
%! patch (fv);
%! axis auto;   # Kludge required for Octave
%! axis equal;
%! grid on;
%! title ("shrinkfaces() does not work on concave shapes");

%!demo
%! clf;
%! [phi r] = meshgrid (linspace (0, 1.5*pi, 16), linspace (1, 2, 4));
%! tri = delaunay (phi(:), r(:));
%! v = [r(:).*sin(phi(:)) r(:).*cos(phi(:))];
%! p = patch ("Faces", tri, "Vertices", v, "FaceColor", "none");
%! fv = shrinkfaces (p);
%! patch (fv);
%! axis auto;   # Kludge required for Octave
%! axis equal;
%! grid on;
%! title ("shrinkfaces() on 2-D complex shapes tessellated with triangles");

%!demo
%! clf;
%! N = 10;  # N intervals per axis
%! [x, y, z] = meshgrid (linspace (-4,4,N+1));
%! val = x.^3 + y.^3 + z.^3;
%! fv = isosurface (x, y, z, val, 3, z, "noshare");
%!
%! p = patch ("Faces", fv.faces, "Vertices", fv.vertices, "FaceVertexCData", ...
%!            fv.facevertexcdata, "FaceColor", "interp", "EdgeColor", "black");
%! axis auto;   # Kludge required for Octave
%! axis equal;
%! view (115, 30);
%! drawnow ();
%! shrinkfaces (p, 0.6);
%! title ("shrinkfaces() on 3-D complex shapes");

%!shared faces, vertices, nfv, nfv2
%! faces = [1 2 3];
%! vertices = [0 0 0; 1 0 0; 1 1 0];
%! nfv = shrinkfaces (faces, vertices, 0.7);
%! nfv2 = shrinkfaces (nfv, 1/0.7);
%!assert (isfield (nfv, "faces"))
%!assert (isfield (nfv, "vertices"))
%!assert (size (nfv.faces), [1 3])
%!assert (size (nfv.vertices), [3 3])
%!assert (norm (nfv2.vertices - vertices), 0, 2*eps)

## Test input validation
%!error <Invalid call> shrinkfaces ()
%!error <Invalid call> shrinkfaces (1,2,3,4)
%!error [a,b,c] = shrinkfaces (1)
%!error <scale factor must be a positive scalar> shrinkfaces (nfv, ones (2))
%!error <scale factor must be a positive scalar> shrinkfaces (nfv, 0)
%!error <only 2-D and 3-D patches are supported> shrinkfaces (faces, ones (3,1))
%!error <only 2-D and 3-D patches are supported> shrinkfaces (faces, ones (3,4))
%!error <faces must consist of at least 3 vertices> shrinkfaces (faces(1:2), vertices)